Question: Karatsubas Algorithm is a divide-and-conquer algorithm for multiplication of large integers which is more efficient than standard Schoolbook methods, at least when the numbers being

  1. Karatsubas Algorithm is a divide-and-conquer algorithm for multiplication of large integers which is more efficient than standard Schoolbook methods, at least when the numbers being multiplied are very large. Suppose two integers being multiplied are both n-bits long. The algorithm makes three recursive calls of size n/2 and performs non-recursive work requiring theta(n) time.

  1. Determine the running time of Karatsubas Algorithm using a recursion tree and substitution (induction).

  2. Determine the running time of Karatsubas Algorithm using the Master Theorem.

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